Exercise · ZW-CONSERVATIVE-FIELD-001 · ★☆☆ Basic
A potential function of the field \(\mathbf F=\langle 2x,\,2y\rangle\) is:
Choose one option.
Show answer
- B. \(f=x^2+y^2\)
Explanation
Since \(\nabla(x^2+y^2)=\langle2x,2y\rangle\), that \(f\) is a potential. \(2x^2+2y^2\) would give \(\langle4x,4y\rangle\).
Review the concept: Conservative field
A vector field \(\mathbf F\) is conservative if it is the gradient of a scalar function \(f\), called a potential function of \(\mathbf F\).
\[\mathbf F=\nabla f\]
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